GATE 2022 ES – Question 10

General Aptitude · Spatial Aptitude: Spatial Reasoning and Visualization · 2 marks · Multiple choice

In the square shown, P, Q, R, S mark its corners and T its center. X is a 180° rotation about diagonal SQ;Y a 180° rotation about diagonal PR;Z a 90° clockwise rotation about the perpendicular axis through T. Compare the left-to-right sequences (1)XYZZ,(2)XY,(3)ZZZZ. Which is correct?

(1) and (2) are equivalent.
(1) and (3) are equivalent.
(2) and (3) are equivalent.
All three are equivalent.

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Show answer and explanation

Correct answer: (B) (1) and (3) are equivalent.

Explanation

On the square’s plane, X and Y act as reflections in perpendicular diagonals. Their composition is a 180° planar rotation, Z². Thus XYZZ=Z⁴=identity, while XY=Z² and ZZZZ=identity. Only sequences (1) and (3) agree. **B**.

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